The standard profit-maximizing multiunit auction intersects the submitted demand curve with a preset reservation supply curve, which is determined using the distribution from which the buyers' valuations are drawn. However, when this distribution is unknown, a preset supply curve cannot maximize monopoly profits. The optimal pricing mechanism in this situation sets a price for each buyer on the basis of the demand distribution inferred statistically from other buyers' bids. The resulting profit

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... converges to the optimal monopoly profit with known demand as the number of buyers goes to infinity, and convergence can be substantially faster than with sequential price experimentation. (